Find the Arc Length Function for the Curve $y=10 x^{3 / 2}$

question 46

Multiple Choice

Find the arc length function for the curve $y=10 x^{3 / 2}$ with starting point $P_{0}(1,15)$ .

• A) \(L=\frac{2}{675}\left((1+225 x)^{3 / 2}+226\right)\)
• B) \(L=\frac{2}{225}\left((1+220 x)^{3 / 2}-226 \sqrt{226}\right)\)
• C) \(L=\frac{2}{675}\left((1+225 x)^{5 / 2}+226 \sqrt{226}\right)\)
• D) \(L=\frac{2}{675}\left((1+225 x)^{3 / 2}-226 \sqrt{226}\right)\)
• E) \(L=\frac{2}{675}\left((1+225 x)^{1 / 2}-226 \sqrt{226}\right)\)

Understand the relationship between perimeter and area of a rectangle and apply this understanding to solve inequality problems related to dimensions of geometric shapes.

Solve inequalities involving algebraic expressions.

Develop the ability to round numerical answers to a specified degree of accuracy.

Apply mathematical reasoning to determine the bounds within which a geometric dimension must lie.

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